VaRES (version 1.0.1)

FR: Freimer distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Freimer distribution due to Freimer et al. (1988) given by $$\begin{array}{ll} &\displaystyle {\rm VaR}_p (X) = \frac {1}{a} \left[ \frac {p^b - 1}{b} - \frac {(1 - p)^c - 1}{c} \right], \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{a} \left( \frac {1}{c} - \frac {1}{b} \right) + \frac {p^b}{a b (b + 1)} + \frac {(1 - p)^{c + 1} - 1}{p a c (c + 1)} \end{array}$$ for \(0 < p < 1\), \(a > 0\), the scale parameter, \(b > 0\), the first shape parameter, and \(c > 0\), the second shape parameter.

Usage

varFR(p, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE)
esFR(p, a=1, b=1, c=1)

Arguments

p

scaler or vector of values at which the value at risk or expected shortfall needs to be computed

a

the value of the scale parameter, must be positive, the default is 1

b

the value of the first shape parameter, must be positive, the default is 1

c

the value of the second shape parameter, must be positive, the default is 1

log

if TRUE then log(pdf) are returned

log.p

if TRUE then log(cdf) are returned and quantiles are computed for exp(p)

lower.tail

if FALSE then 1-cdf are returned and quantiles are computed for 1-p

Value

An object of the same length as x, giving the pdf or cdf values computed at x or an object of the same length as p, giving the values at risk or expected shortfall computed at p.

References

S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted

Examples

# NOT RUN {
x=runif(10,min=0,max=1)
varFR(x)
esFR(x)
# }